Bird's eye view of temperaments by accuracy: Difference between revisions
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The bound is the approximate [[JND|melodic JND (Just-Noticeable-Difference)]], though note that this doesn't mean that damage/mistuning is ''imperceptible'' in these temperaments as the harmonic JND can often be significantly smaller, depending largely on context, timbre and who is listening/who you ask. | The bound is the approximate [[JND|melodic JND (Just-Noticeable-Difference)]], though note that this doesn't mean that damage/mistuning is ''imperceptible'' in these temperaments as the harmonic JND can often be significantly smaller, depending largely on context, timbre and who is listening/who you ask. | ||
== 5-limit focus == | == 5-limit focus == | ||
=== [[Sensipent]] === | |||
Note counts: | |||
* 10 for {3, 5, 31} ([[8L 3s]]) | |||
* 19 for {3, 5, 9, 15, 25, 31} ([[8L 11s]]) | |||
Sensipent is an accurate 2.3.5.31 temperament with a generator of [[~]][[31/24]][[~]][[40/31]], where the two interpretations of the generator differ by [[961/960|S31 = (31/30)/(32/31)]], which is the best extension of 5-limit sensipent as its generator serves as half of 40/24 = [[5/3]], so that the generator is the midpoint of [[4/3]] and [[5/4]], whose difference is [[16/15]], hence the relevance of making [[~]][[32/31]][[~]][[31/30]]. | |||
Sensipent finds [[6/1]] (the fifth plus two octaves) at 7 generators. | |||
It admits a number of extensions of varying accuracy: | |||
* the most accurate is [[#Sendai]] which finds primes 23 and 29 | |||
* the second most accurate is [[#Sensible]], which finds primes 11, 17 and 23 | |||
* the simplest but least accurate is [[#Sensor]] (commonly just called "sensi"), which interprets it as a full 17-limit temperament. | |||
=== [[Würschmidt]] === | === [[Würschmidt]] === | ||
Note counts: | Note counts: | ||